Seismic surveying



Patented Apr. ll, i944 ,U Nis STATES PATENT OFFICE SEISMIC SURVEYING Joseph'l). Eisler, Tulsa, Okla", assignor to Stanclind Oil and Gas Company, Tulsa, Okla., a corporation of Delaware Application February 28, 1942, Serial No. 432,869

3 Claims. (01. 177-352) I 'I'hisinvention pertainsjto the art of seismicsurv'eying'and more particularly to'improvements in'the distortionless' recording of the'waves re-.

ceived by aIseismometer in a 'process'of such surveying.-

-It is customary in present day practice of this art to'einploy filters interposed at some point between the'seismometer and the recorder in order to" eliminate the low frequency extraneous waves which are generated in the seisinometer by ground roll-or'the like and the high frequencies due to such-effects as wind, microseisms and microphonics of the cable between the 'seismometers and therecording truck, etc. I The II use of such filters inthe'prior art hasgen'erally resulted in than that present in the input to the filters. Likewise an average time delay is interposed which increasing the ratio'of 'the desired signal to extraneous'" n6ise' but}. on the other hand, I have found that the indiscriminate use of such, filters has caused phase distortionfin the recording.

It. is an object of this invention to provide seismic surveying apparatus bymeans of which the desired i'eilecteci seismic waves which have I been-changed into electricalwaves are filtered to remove undesirable "lowi, and high frequencies without introducing'phase distortion prior to the step of recording said waves. 'It" is afurther I object" of this invention to provide a particular,

design of filters for use'in'seismic surveying recording apparatus by means of which electrical invention will be apparent from a reading of this- In" the past .the de'sig n of"electrical frequency" discriminating networks used in suppressing'the varies from one set of filters of one particular design to-another so that an undesirable time lag appears in the resultant record. The ideal sys- .tem should make-it possible to record the desirable frequency componentsof the ground motion while. preserving the time relationship of these components after they impinge upon the seismometer. An additional advantage of such a system is the possibility of correlating records obtained using filters of various discriminations without distorting the complex wave patterns provided these filters have overlapping amplitude response characteristics. After considerable experimentation I have found that a recording system a proaching the ideal can be realized if certain relationships are observed in designing the filter elements in these seismic recording systems. When these relationshipsare observed, it is possible to design seismic recording systems which have practicallyno phase distortion throughout the desired band of frequencies tobe recorded and furthermore it is possible to employ various widths of pass band waves of various'frequnciespassed b this filter are delayed snequsi period p'f'tiine and by' means ground motions s'iicl'i-as those dueltofground roll I and wind have been efie'ctedcnthe basis of amplitude responsaonly." In general: filters passing waves the'freque'ncy of which are in the'range between approximately- 20 cycles'per second and 150 cycles per 'sec'ond have been used. Amplitude responses covering various portions Of I the useful frequency spectrum have been used in different sections ofthe country. However, I have found that the indiscriminate use of such filters leads to a distortion which has not been recog nized by the art. I

The ideal system of frequency discrimination possesses the property of discriminatin against unwanted frequencies without introducing phase or timeuiela distortion' By' phase'distortion, is

meant the phenomenonbcc'urrin inisuch filters in which-frequency components of a particular .without disturbing this relationship. I II In order to illustrat the invention more completely, certain drawings have been appended heretoand'made a part hereof. In these figures the same reference numeral refers to the same or a corresponding part.

Figure l'represents in diagrammatic form'a recording system for use in seismic surveying employing vone embodiment of my invention;

Figure 2 is a diagram of a generalized band passfilter'; I

Figure 3 isa wiring diagram of one variety of band pass filter;

Figure 4 is a graph ofthephaseQ characteristic of a band pass filter; and

, Figure 5'i's a diagrammatic representationof an alternative seismic recording system utilizing another embodiment of my invention. I I

' Referring now to Figure 1': a seismometer. I I is shown resting on'the surface of the und 12 in the region in which the s'eismicjinvestigw' 'tion is to bevcarried'on. .This seismometer is con- I nected by conductors l3 to an input transformer f H in the recording truck. The secondary of this transformer I4 is connected between cathode and grid of vacuum tube l5, which may for example I be a pentode as shown-the cathode of which is connected to a biasing circuit comprising resistance l6 and condenser ll. The screen grid of this tube is energized from a battery I 8 or other source of potential, preferably but not necessarily through a filter resistance and filter condenser indicated generally by numeral IS, the other side of which is grounded. The output of this vacuum tube is coupled by means of a filter indicated generally by numeral 20 to the grid of a second vacuum tube 2|. The cathode of th second vacuum tube 2i is suitably biased by means of a cathode resistance 22 across which is a shunt condenser 23. The output of this tube 21 is coupend upon the use of such device. The filaments of both vacuum tube IS and vacuum tube 2| are connected at points X!! to a suitable source of potential such as a storage battery.

In operation a charge of dynamite is exploded in the ground. The refracted, reflected and ground waves energizethe seismometer l I, settin up electric waves which includethe components which are to be recorded. These components usually fall somewhere in the range'between about 20 cycles per second and 150 cycles per second. The useful frequency spectrumvaries from one region to another and quite often desirable information can be obtained only if certain unwanted frequencies are suppressed. The electric waves pass through the transformer ll into the amplifier tube I 5, where they are amplified and pass into the band pass filter 2|, at which point the undesirable frequency components are eliminated. and then through the amplifier tube v2| into the recorder. Usually the gain control is set in such fashion that the output to the recorder is more or less uniform regardless of the strength of the incoming signals.

It is found that when an electric wave passes through a band pass filter, in general there will be a time delay interposed so that the output signal lags behind the input signal. If the time delay is not uniform for all of the frequency components of the signal, the output wave will be distorted by the filter even though all of the components of the input wave are within the pass band of the filter. This phenomenon of distortion due to time delay which can be conveniently described as time-delay or phase distortion is relatively unimportant in most of the filter apsired signals.

The phenomenon of time delay distortion can be discussed inconnection with various types of filters, but it is perhaps most easily understood by a discussion of the type of filters which I prefer to use in this invention; namely, the variety lmown as the constant-K" type filter.- In Figure 2 I have shown a wiring diagram of a section of one generalized type of filter commonly known as a T section with two series arms and one shunt arm terminating in'the iterative or characteristic impedance Z0. The impedance of each series arm is and the impedance of the shunt impedance is Zn. In the constant-K type of filter the product of Z122 is a constant. The terminating iterative impedance for correct operation is given by Z2 ZO=:/ZIZZ+ZL The signal is introduced, for example, in series with the input impedance Z0. This is represented in Figures 2 and 3 by a zero impedance source of E. M. F. 32. When such a filter is made up of a series resonant circuit for each of the series arms and a parallel resonant circuit for the shunt arm in the manner shown in Figure 3 with the product of the inductance 28 and the capacity 29 in each series arm equal to th product of the for example. Communication Engineering, by

Everitt, p ges 151 to 178. Note that in Figure 1. resistance 38 and th plate resistance of vacuum tube IS in parallel, mustequal the iterative impedance 34 in Figure 3.

When pure sine waves of various frequencies are impressed on the filter by generator 32, it is found that only at one frequency is the output across the terminating impedance 32 in phase with the input signal. This occurs at the angu lar mid frequency Wm. Within the pass band, that is from lower cut-oil. angular frequency or to upper cut-oi! angular frequency on, I have found. that the phase difleren'ce between the input and output signals varies approximately lineter consists of two or more frequencies, it is necessary, as discussed above, to delay each frequency component of the wave by the same amount when passing it through the filter if no phase distortion is to be obtained. The phase shift ,8 is related to the time delay At for any single frequency by the expression At= m where m is the angular frequency of the signal I component in radians per second ands is thephase angle in radians. To have the delay time for all frequency components the same; it is necessary that At be constant: hence the phase shift p must vary linearly with w. This condition is satisfied in the pass band of a constant-K band pass filter. Therefore, there will be the same delay time along all components of a complex wave sothat this type of phasev distortion is thereforeeliminated when such a filter is eme=Ei sin wat+Ez sin mt where both a: and :4 lie in the pass band of the filter. By referring to Figure 4 it is seen that the corresponding phase shifts at the frequencies w: and we are 63 and 54. The output signal will therefore be It can be easily seen that when Bu=i2n1r where n is an integer (including zero) the expression for e becomes 8'=E1 sin (criticism) +32 sin (mtiwrm) e'=E1 sin wsdim) +E2 sin wdtzL-ml Thus the resultant wave is not distorted with respect to the input wave but is simply delayed by m which is the slope of the phase shift characteristic.

If flo=:Ln-s' where n is an odd integer the only change will be that a negative sign must be placed in front of E1 and E: so that the output signal will still be undistorted but will be inverted with respect to the input signal. Therefore, if a filter is designed with an apparent phase shift at zero frequency (B0) of an odd integral mul tiple of 1r, the output terminals of the filters are reversed with respect to the input terminals be fore the filter is-used.

The two criteria for absence of time delay or phase distortion are, therefore, that the phase shift characteristic be linear with frequency and integral multiple oflr, preferably an integral multiple of 21, said integral multiple including the value of zero.

I have found that only certaimrelationships have already, beendeveloped "flu must be 1hr where r is an integer, preferably an even integer. From Figured it can be seen thatin this case, from similar triangles V UL 002 so that M T -fir where n is an integer. Only filters with ratios of the cut-off frequencies which approximately sat-' isfy the above formula, and the phase shift of which in the band pass vary approximately linearly with frequency, are therefore free from phase distortion. a In a simple band pass filter such as that shown in Figure l, I have found that the absolute valbetween the frequencies at the edge of the pass band, i. e. the frequencies of upper and lower cut-off are possible in order to obtain this freedom from phase distortion. This is a consideration which has not heretofore been determined and it immediately shows that only certain relationships between these cut-off frequencies are possible in filters used in seismic amplifiers.

From a consideration of the criteria which lies of pi and fin are approximately identical, at a value of about "k. If n is given the value of 2 so that the apparent phase shift at zero frequency has the desired value of 21r radians, it is apparent from this that we must be about twice on or, in other words, the upper cut-off frequency-- must be approximately twice that of the low cut- -off frequency. As a matter of fact, I have found that slight variations from this requirement of the'order of about 5% can be tolerated. Ifn is 1, the apparent phase'shift at zero fre quency is a' radians and the ratio of cut-off frequencies is approximately 4. If H0 is 31' the ratio and p: is not as given in Equation 1 above, the

filter is not distortionless as to phase.

In some cases the band pass filter may be satisfactorily interposed in the seismic recording circuit prior to the amplifier proper. One such arrangement is shown in Figure 5 in which the filter 31 serves as a couplingbetween the input transformer l4.and the vacuum tube 15. A coupling transformer 38 is shown connecting vacuum tubes and 2|, although any desired alternate form of coupling can be employed. The transformer primary can suitably be connected to the plate supply through filter resistance 89 and shunted by condenser 40. It is apparent to those skilled in the art that the band pass filter can be placed as the coupling element between any sections of a multi-vacuum-tube amplifying channel with success and that it is possible, although usually not desirable, to place it as a coupling element between the out-put of the amplifier and the recorder. In this latter case the output impedance is so low that it requires filter components of an excessively large value. The filter works as well whether or not there is a gain control 21 used in connection with the amplifier. One can if desired change from one distortionless filter having a given frequency ratio, for example 2, to another having another ratio, for example. 1.5, without introducing distortion into the system.

In some cases it is desirable to utilizea system in which the overall phase shift characteristic of the system is corrected to remove any phase distortion whatsoever. In such a' case I prefer to design the seismometer and the amplifier with the least phase shift possible in the desired range of frequencies and then apply a filter of the type described above in such a manner that in the entire band passthe variation of system phase shift to those skilled in this art.

015 limiting the application of this'invention to even) multiple off.

Various changes and modifications in the systems described above willbe immediately apparent I have no intention the circuits described above, which were utilized a merely for the purpose of illustration. The in -vent ion is best described in the appended claims.

I claim: 1'. In apparatus for seismic prospecting including a seismometer adapted toproduce electric waves in response to seismic waves, anamplifier for said electric waves, and a recorder for record-- a ing the output of said amplifier, the improvement comprising an electric bandpass filter interposed in said apparatus between said seismometer and said recorder, said filter being so designed and constructed that in the range of frequencies defined by said pass band the phase shift between output from said seismometer and input to. said recorder varies substantially linearly with fre-K queney in such a manner that the apparent phase shift at zero frequency is an integralmultiple of 'r radians.

I 2. In. apparatus for' seismic prospecting including a s'eismometer adapted I to produce electric waves in response to seismic waves, an amplifier for said electric waves, and a recorder for recording the output of said amplifier, the improvement comprising an electric constant-K type band pass filter interposed insaid apparatus between said seismometere and said recorden'said'filter'being so designed and constructed that in the range of frequenciesdefined by said pass band the phase shift between input to said filter and output from said I I filter varies approximately linearly with 'frequency insuch a manner that the-apparent phase shift at zero frequency is an integral multiple of r filter interposed in said apparatus between said seismometerand said amplifier, said filter being so designed and constructed that in the range of frequencies defined by said pass band the phase shift betweeninput to said filter and output from, said filter varies substantially linearly with fre- I quency and in which filter the ratio of frequency at upper cut-off fztofrequency at lower cut-off f1 is given approximately by the formula V 7 5! where n is an integer, and fiz and p; are the phase shift angles at the frequencies f2 and f1 respectively,

JOSEPH D. EISLER. 

